Tower Defense中文
A small Unity tower defense game, playable right in the browser.
Artificial Intelligence
Search, logic, Bayesian networks, and probabilistic inference.
Bobby’s Knowledge Base
Course notes written as I learn. Definitions and theorems are set apart from the discussion, and chapters have a review mode for testing yourself. Alongside them are a few essays and things I have built.
Theorem 2.12
Strong Law of Large Numbers
Let \(X_1, X_2, \ldots\) be i.i.d. random variables with \(\mathbb E|X_i| < \infty\). Let \(\mathbb E X_i = \mu\) and \(S_n = X_1 + \cdots + X_n\). Then
\[ \frac{S_n}{n} \xrightarrow{\mathrm{a.s.}} \mu \qquad \text{as } n \to \infty. \]
A theorem as it appears in Applied Probability.
Search, logic, Bayesian networks, and probabilistic inference.
Geometric representations, transformations, rasterization, shading, and ray tracing.
Optimization, generalization theory, and supervised learning.
Measure-theoretic probability: integration, independence, conditional expectation, and laws of large numbers.
Supervised learning, generative models, and sequence modeling.
Mechanics, thermal physics, electromagnetism, and relativity.
Probability, concentration, generating functions, and optimization.
Vector spaces, linear maps, determinants, spectral theory, and canonical forms.
Limits, derivatives, integrals, vector calculus, and series.
2026.10.25 Games · Projects
A small Unity tower defense game, playable right in the browser.
2026.09.13 Music
A structured reference for rhythm, notation, intervals, scales, harmony, and musical analysis.
2026.05.29 AI · Projects
How to express real requirements clearly and use AI to build better presentations more efficiently.